We describe a new approach to Johnson Noise Thermometry(JNT) that takes advantage of recent advances in Josephson voltage standards and digital signal processing techniques. Currently, high-precision thermometry using Johnson noise is limited by the non-ideal performance of the electronic measurement system. By using the perfectly quantized voltage pulses from a series array of Josephson junctions, any arbitrary broadband waveform can be synthesized and used as a calculable noise source for calibrating the cross-correlation electronics used in JNT systems. With our prototype JNT system, we have found agreement between the voltage noise of a 100 W resistor in a triple-point Ga cell (T90 = 302.916) and the pseudo noise waveform that has the same average power and is synthesized by a Quantum Voltage Noise Souce (QVNS) to be within 2 parts in 103 with a 1s uncertainty of 1x10-3. We estimate the temperature of the resistor to be 302.5 K 1 0.3K (1s uncertainty based on the uncertainty from the cross correlation). With better characterizaion of our JNT system, we should be able to achieve relative accuracies of parts in 105 for an arbitrary temperature in the range between 270 K and 1000 K.